# It may take another 2016 years?

Consider a polynomial

$\large f(x)=x^{2016}-x^{2015}+x^{2014}-x^{2013}\ldots-x^1+x^0$

Then find

$\large f(2016)-f(2015)+f(2014)-f(2013)\ldots-f(1)+f(0)$

You can also post any other problems related to functions.

Note by Anish Harsha
5 years, 7 months ago

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- 5 years, 7 months ago

Uhh... congratulations? Actually, how on earth did you get that?

- 5 years, 7 months ago

wolframalpha

- 5 years, 6 months ago

The answer is indeterminate because $f(0) = 0^{2016} - 0^{2015} + \cdots + \color{#D61F06}{0^0}$.

- 5 years, 7 months ago

Then what will be the answer if we take out $f(0)$, sir ?

- 5 years, 7 months ago

Hint: $\dfrac{x^n + 1}{x+1} = x^{n-1} - x^{n-2} + x^{n-2} - \cdots + 1$ for positive odd $n$.

- 5 years, 7 months ago

2016

- 5 years, 7 months ago